X₂₈₄

X₅₅-CROSS CONJUGATE OF X₂₁

X₂₈₄ = isogonal conjugate of X₂₂₆

5, 6, 7 3, 4, 5 Kepler Kimberling

X₂₈₄ (X₅₅-CROSS CONJUGATE OF X₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {3, 6}, {1, 19}

• Related Centers: X₅₅ (INSIMILICENTER), X₂₁ (SCHIFFLER POINT), X₃ (CIRCUMCENTER), X₆ (SYMMEDIAN POINT), X₁ (INCENTER), X₁₉ (CLAWSON POINT)

Trilinears: \((\sin A)/(\cos B + \cos C) : (\sin B)/(\cos C + \cos A) : (\sin C)/(\cos A + \cos B)\)

Barycentrics: \(a^{2}/(\cos B + \cos C) : b^{2}/(\cos C + \cos A) : c^{2}/(\cos A + \cos B)\)

Search Value (6, 9, 13): \(2.260890629888\)

▸ Alternate Coordinates1 form

• Trilinears: \(a (b + c - a)/(b + c) : :\)

▸ Linear Combinations1 combination

• X₂₈₄ = \(s\) X₃ + \((r + 2R) \cot(\omega )\) X₆

▸ Incident Central Lines21 lines

{1, 19}, {2, 272}, {3, 6}, {9, 21}, {27, 226}, {29, 950}, {35, 71}, {37, 101}, {55, 219}, {57, 77}, {60, 283}, {73, 951}, {86, 142}, {102, 112}, {109, 296}, {163, 909}, {198, 859}, {261, 332}, {405, 965}, {501, 942}, {515, 1065}

▸ Functional Relations15 relations

• X₂₈₄ = isogonal conjugate of X₂₂₆

• X₂₈₄ = isotomic conjugate of X₃₄₉

• X₂₈₄ = anticomplement of X₁₇₀₅₂

• X₂₈₄ = inverse-in-Brocard-circle of X₅₇₉

• X₂₈₄ = X_i-Ceva conjugate of X_j for these (i,j): (81, 58), (333, 283)

• X₂₈₄ = cevapoint of X_i and X_j for these (i,j): (6, 48), (41, 55)

• X₂₈₄ = X₅₅-cross conjugate of X₂₁

• X₂₈₄ = crosspoint of X_i and X_j for these (i,j): (21, 81), (29, 333)

• X₂₈₄ = crosssum of X_i and X_j for these (i,j): (37, 65), (73, 1400)

• X₂₈₄ = crossdifference of every pair of points on line X₅₂₃X₆₅₆

• X₂₈₄ = trilinear pole of line X₆₅₂X₆₆₃

• X₂₈₄ = X₉₂-isoconjugate of X₇₃

• X₂₈₄ = X₁₅₇₇-isoconjugate of X₁₀₉

• X₂₈₄ = perspector of ABC and unary cofactor triangle of Gemini triangle 10

• X₂₈₄ = perspector of ABC and unary cofactor triangle of isogonal triangle of X₁ (a.k.a. reflection triangle of X₁)